What Makes a Good Problem? Perspectives of Students, Teachers, and Mathematicians

While mathematical problem solving and problem posing are central to good mathematics teaching and mathematical learning, no criteria exist for what makes a good mathematics problem. This grounded theory study focused on defining attributes of good mathematics problems as determined by students, teachers, and mathematicians. The research questions explored the similarities and differences of the responses of these three populations. The data were analyzed using the grounded theory approach of the constant comparative method. Fifty eight students from an urban private school, 15 teachers of mathematics, and 7 mathematicians were given two sets of problems, one with 10 algebra problems and one with 10 number theory problems, and were asked choose which problems they felt were the “best” and the “least best”. Once their choices were made, they were asked to list the attributes of the problems that lead to their choices. Responses were coded and the results were compared within each population between the two different problem sets and between populations. The results of the study show that while teachers and mathematicians agree, for the most part, about what attributes make a good mathematics problem, neither of those populations agreed with the students. The results from this study may be useful for teachers as they write or evaluate problems to use in their classes.